Polynomial inequalities for non-commuting operators

We prove an inequality for polynomials applied in a symmetric way to non-commuting operators

Elementary operators and their lengths

Elementary operators on an algebra, which are finite sums of operators $x \mapsto axb$, provide a way to study properties of the algebra. In particular, for C*-algberas we consider results that are related to the length $\ell$ of the operator, defined as the minimal number of summands required. We will review some results concerning complete positivity or complete boundedness. Although all elementary operators on a C*-algebra $A$ are completely bounded, that is induce uniformly bounded operators on the algebras $M_n(A)$, the supremum is always attained for $n =\ell$, or for smaller $n$ in case $A$ has special structure. For positivity, there are also results couched in analagous terms, but with different bounds. In recent work with I.~Gogi\\u27c, we have shown that for prime C*-algebras $A$ the elementary operators of length (at most) $1$ are norm closed, but that for the rather tractable class of homogeneous C*-algebras more subtle considerations are required for closure. For instance $A = C_0(X, M_n)$ fails to have this closure property if $X$ is an open set in $\mathbb{R}^d$ with $d \geq 3$, $n \geq 2$ ($X \neq \emptyset$)

Norms and CB norms of Jordan elementary operators

AbstractWe establish lower bounds for norms and CB-norms of elementary operators on B(H). Our main result concerns the operator Ta,bx=axb+bxa and we show ‖Ta,b‖⩾‖a‖‖b‖, proving a conjecture of M. Mathieu. We also establish some other results and formulae for ‖Ta,b‖cb and ‖Ta,b‖ for special cases

Non-commutative automorphisms of bounded non-commutative domains

We establish rigidity (or uniqueness) theorems for non-commutative (NC) automorphisms that are natural extensions of classical results of H. Cartan and are improvements of recent results. We apply our results to NC domains consisting of unit balls of rectangular matrices

A Time Stretching and pitch shifting windows phone application

Document is abstract submission for conference, see pdf downloa

Optically probing the detection mechanism in a molybdenum silicide superconducting nanowire single-photon detector

We experimentally investigate the detection mechanism in a meandered molybdenum silicide superconducting nanowire single-photon detector by characterising the detection probability as a function of bias current in the wavelength range of 750–2050 Onm. Contrary to some previous observations on niobium nitride or tungsten silicide detectors, we find that the energy-current relation is nonlinear in this range. Furthermore, thanks to the presence of a saturated detection efficiency over the whole range of wavelengths, we precisely quantify the shape of the curves. This allows a detailed study of their features, which are indicative of both Fano fluctuations and position-dependent effects